Do you want to know? It's not a matter of SHOULD. I like to know when my partners start a sexual relationship with someone new but outside that I have very little desire to know details. For me it feels like I'm intruding on something personal between them.

Also is he comfortable with having his sex life shared with you? Although you share a partner there might be some things he wishes to keep private and his wishes should be respected. If these are things that he would tell you directly then there's probably no concern in your shared partner sharing the details with you.